Bump map causes strange shading
Given the image, and the fact that subdivisions help, I'm inclined to say that it's a terminator problem.
Sadly, it's a common problem on most ray/pathtracers, so your solutions are:


Increase subdivisions.
Increase light sizes. This will make shadows softer, and will mask the problem a bit.
Use a non-tracer renderer (like Blender Internal or, maybe Eevee), that doesn't have this problem.